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Introductory undergraduate topics to teach sixth form

Discussion in 'Mathematics' started by bobdrivesahgv, Mar 24, 2016.

  1. bobdrivesahgv

    bobdrivesahgv New commenter

    If you had the time - a spare hour, a "session 6", etc - and a motivated bunch of volunteers aiming to go on to do maths degrees, which introductory topics might you teach for a bit of a delve into what they can expect to see?

    I'm thinking first courses in linear algebra and complex variables, but am keen to hear others' opinions.
     
  2. PaulDG

    PaulDG Occasional commenter

    How confident are you that they're going to get 600UMS in both Maths& FM A level? And a level 2 in STEP 2 or 3?

    If you're not confident of those, there's more to do before jumping the gun to undergraduate work, isn't there?
     
    bobdrivesahgv likes this.
  3. adamcreen

    adamcreen Occasional commenter

    My Year 8 Masterclass on Group Theory (4 hours covering transformations of the unit square, permutation groups, modulo arithmetic, classifying groups of order n, and subgroups) would be ideal for this. I really benefited from doing Group Theory in my A Level (1986-88) before Uni as it meant I had concrete examples of what rapidly became theoretical and inaccessible otherwise.
     
    bobdrivesahgv likes this.
  4. bobdrivesahgv

    bobdrivesahgv New commenter

    Thanks. :)
    Group theory is a lovely example.
    That's a great idea, which hadn't immediately come to my mind.
     
  5. Piranha

    Piranha Star commenter

    Little extensions on what they are doing can be good. E.g. what convergence really means or proof of the countability of rationals and uncountability of real numbers. Groups sound interesting if you have the time.
     
  6. Owen134866

    Owen134866 New commenter

    I would make use of the mentoring materials provided each month by the UKMT - they have similar stuff available for younger pupils as well. I think this kind of general problem solving would be a better way to stretch their thinking skills, rather than just teaching more 'knowledge', if you get my meaning! :)

    https://www.ukmt.org.uk/mentoring/
     
    bombaysapphire likes this.

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